Abstract
Let ∧⊂⊂ Ω⊂ \(\widetilde\Omega\) where \(\widetilde\Omega\) is the domain of definition of the solution of an elliptic equation. One assumes certain conditions of regularity on the equation and on the finite elements on Ω. Then one shows that the L2 (Ω) convergence of the approximate solution towards the exact solution implies the L∞ (∧) convergence with the same order.
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Descloux, J., Nassif, N. (1977). Interior L∞ estimates for finite element approximations of solutions of elliptic equations. In: Galligani, I., Magenes, E. (eds) Mathematical Aspects of Finite Element Methods. Lecture Notes in Mathematics, vol 606. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064456
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DOI: https://doi.org/10.1007/BFb0064456
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